Apply rotation to camera?
The suggested YXZ order from the video does not work in Blender because it uses the Z up axis convention, whereas Maya uses Y as up axis.

If you want to get a setup like the video, where the gimbal lock occurs when looking up or down, you need to parent the camera to an empty and rotate the empty 90° on the X axis, then set the rotation order on the camera to YXZ.

Only changing the rotation order on the camera can't work, the gimbal lock always happens at 90° on some axis and the camera is at (0°, 0°, 0°) when looking down, so this extra parenting is needed.

That being said, I think the standard XYZ rotation order in Blender may actually be better for cameras. It will give you gimbal lock when tilting the camera 90° sideways, which is perhaps even less common than looking down or up.